Individuals often have the need to visually convey information to others. In the past, standard tables and charts have been used to express such information. A standard table consists of a systematic arrangement of rows and columns of interrelated data. An example of such a table is shown below in Table 1.
TABLE 1Motion of a ProjectilePosition on XPosition on YAxis (ft)Axis (ft)001426374653
A standard chart consists of a graphical representation of the relationships between two or more interrelated variables. An example of such a chart, depicting the corresponding X and Y coordinates of a moving projectile, is shown in FIG. 1.
Generally, all of the entries in a standard table are presented in the same format. For example, all entries in the table of FIG. 1 have the same font (Times), the same font size (12 point), and the same font color (black). Thus, it is difficult to emphasize certain entries within standard tables.
Similarly, all of the markers in a standard chart are also normally presented in the same format. For example, all of the markers in the chart of FIG. 1 have the same line width (0.75 point), the same marker size (⅛ inch), and the same marker shape (circular). Thus, it is also difficult to emphasize entries within standard charts.
It is often desirable to visually demonstrate the relationships between more than two interdependent variables in a table. For example, in the projectile example discussed above, the user may wish to present information regarding the movement of the projectile along a Z-axis perpendicular to both the X-axis and the Y-axis (i.e., use a two-dimensional table for a three-dimensional representation). In addition, the user may wish visually represent information concerning the time, after the object is set into motion, at which the projectile reaches each point along the X-axis.
Traditionally, the relationships between four interdependent variables have been depicted in a tabular format by creating a table having four columns; one column for each independent variable. Thus, in the example discussed above, an author could use known methods to create a table depicting the relationships between the four interdependent variables (X-position, Y-position, Z-position, and time) by adding two new columns to the table shown in FIG. 1. Such a table is shown below as Table 2. The disadvantage of this technique is that it makes the table larger and more complex than a table having fewer columns.
TABLE 2The Motion of a Projectile including Z-Coordinates and TimePosition onPosition YPosition onTimeX Axis (ft)Axis (ft)Z Axis (ft)(seconds)000014−1126−1237−1346045315
It is also often desirable to visually demonstrate the relationships between more than two interdependent variables in a two-dimensional chart. Traditionally, authors have depicted the relationships between three interdependent variables in a chart by first creating a two-dimensional chart to display the relationship between two of the interdependent variables, as shown in FIG. 2, and then coloring the chart's markers to represent the relationship between the third interdependent variable and the two variables already depicted. Such a technique is commonly used in topographical maps to indicate changes in elevation.
Thus, returning to the example above, an author could use known techniques to indicate the Z-position of the projectile in the chart of FIG. 2 by first establishing a legend of colors corresponding to various Z-coordinates and then coloring each of the markers according to the legend. An example of such a technique is shown in FIG. 2 below.
Authors have not been successful in developing an elegant technique for displaying the relationships between four or more interdependent variables in a two-dimensional chart. Authors often indicate values of a fourth variable by writing the value of the fourth variable next to the appropriate marker as shown below in FIG. 3. However, such a technique causes charts to be cluttered and difficult to read.
Thus, there is a need for a method for emphasizing certain entries in visual representations of information such as tables and charts. There is also a need for a method for increasing the amount of information that can be displayed within a table without increasing the physical size of the table. Similarly, there is a need for a method of increasing the amount of information that can be displayed within a chart without making the chart difficult to read. Thus, there is a need for a method of increasing the information density within a table or a chart. There is also a need for a method of efficiently representing the interrelationships between four or more interrelated variables in a two-dimensional chart.